The temperature dependence of the parallel upper critical field for a layered superconductor on an insulating substrate is calculated within the framework of the de Gennes-Werthamer theory. The resultant upper critical field curve is shown to be strongly dependent upon the presence of the free surface and the character of the initial layer. A direct comparison of the calculated upper critical field curves with the experimental results of Maj and Aarts on Nb/NbZr layered structures is given. The results are in good agreement provided the pair-breaking effect of the electron-spin paramagnetism is included